Mar 28, 2024  
2017-2018 Undergraduate Academic Catalog 
    
2017-2018 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 385 - Modern Algebra with Applications

3 lecture hours 0 lab hours 3 credits
Course Description
This course is an introduction to abstract algebra with a focus on elementary group theory and some of its applications. Topics include: modular arithmetic, groups, subgroups, isomorphism, external direct products, rings, integral domains and fields. Applications include: error checking/correction and the RSA encryption algorithm. (prereq: MA 235  or equivalent, junior standing)
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Perform modular arithmetic operations including powers and inverses of large numbers
  • Identify whether or not a set together with a binary operation is a group
  • Relate divisibility facts to properties of cyclic groups
  • Identify isomorphic groups
  • Perform arithmetic operations with external direct products of cyclic groups
  • Prove basic theorems involving groups
  • Perform error-checking and error-correction computations including the ISBN system
  • Use the RSA algorithm to encrypt and decrypt large numbers
  • Solve second-degree equations in various rings
  • Prove basic theorems involving rings

Prerequisites by Topic
  • None 

Course Topics
  • Division algorithm, Euclidean algorithm, modular arithmetic and error-checking
  • Binary operations and groups
  • Finite groups and subgroups
  • Cyclic groups
  • Mappings and isomorphisms
  • External direct products
  • RSA encryption and modular arithmetic with large numbers
  • Fundamental Theorem of Finite Abelian Groups
  • Rings
  • Impossible constructions
  • Reviews
  • Exams

Coordinator
Anthony Van Groningen



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